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Rolling
Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding. Rolling where there is no sliding is referred to as ''pure rolling''. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (e.g., a generating line segment of a cylinder) of the rolling object is zero. In practice, due to small deformations near the contact area, some sliding and energy dissipation occurs. Nevertheless, the resulting rolling resistance is much lower than sliding friction, and thus, ro ...
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Rolling Resistance
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses (see below), and permanent (plastic) deformation of the object or the surface (e.g. soil). Note that the slippage between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called slip loss or slip resistance. In addition, only the so-called slip resistance involves friction, therefore the name "rolling ...
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Rolling Animation
Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding. Rolling where there is no sliding is referred to as ''pure rolling''. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (e.g., a generating line segment of a cylinder) of the rolling object is zero. In practice, due to small deformations near the contact area, some sliding and energy dissipation occurs. Nevertheless, the resulting rolling resistance is much lower than sliding friction, and thus, rol ...
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Rolling-element Bearing
In mechanical engineering, a rolling-element bearing, also known as a rolling bearing, is a bearing which carries a load by placing rolling elements (such as balls or rollers) between two concentric, grooved rings called races. The relative motion of the races causes the rolling elements to roll with very little rolling resistance and with little sliding. One of the earliest and best-known rolling-element bearings are sets of logs laid on the ground with a large stone block on top. As the stone is pulled, the logs roll along the ground with little sliding friction. As each log comes out the back, it is moved to the front where the block then rolls on to it. It is possible to imitate such a bearing by placing several pens or pencils on a table and placing an item on top of them. See " bearings" for more on the historical development of bearings. A rolling element rotary bearing uses a shaft in a much larger hole, and cylinders called "rollers" tightly fill the space between ...
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Bearing (mechanical)
A bearing is a machine element that constrains relative motion to only the desired motion, and reduces friction between moving parts. The design of the bearing may, for example, provide for free linear movement of the moving part or for free rotation around a fixed axis; or, it may ''prevent'' a motion by controlling the vectors of normal forces that bear on the moving parts. Most bearings facilitate the desired motion by minimizing friction. Bearings are classified broadly according to the type of operation, the motions allowed, or to the directions of the loads (forces) applied to the parts. Rotary bearings hold rotating components such as shafts or axles within mechanical systems, and transfer axial and radial loads from the source of the load to the structure supporting it. The simplest form of bearing, the '' plain bearing'', consists of a shaft rotating in a hole. Lubrication is used to reduce friction. In the ''ball bearing'' and ''roller bearing'', to reduce slid ...
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Rolling Cone Motion
Rolling cone motion is the rolling motion generated by a cone rolling over another cone. In rolling cone motion, at least one of the cones is convex, while the other cone may be either convex, or concave, or a flat surface (a flat surface can be regarded as a special case of a cone whose apex angle equals \pi). The distinguishing characteristic of a rolling cone, in relation to other axially symmetrical rollers (cylinder, sphere, round disk), is that while rolling on a flat surface, the cone's center of gravity performs a circular motion rather than a linear one. Another unique characteristic is that one of its points (its apex) is at rest throughout the entire motion. Kinematics The motion of a rolling cone can be described as a superposition of a rotational motion of the cone around its axis of symmetry, and a rotary motion of its axis around the axis of symmetry of the stationary cone. The ratio between the angular velocities of these two motions is given by: :\frac = wher ...
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Ball Bearings
A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races. The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads. It achieves this by using at least two races to contain the balls and transmit the loads through the balls. In most applications, one race is stationary and the other is attached to the rotating assembly (e.g., a hub or shaft). As one of the bearing races rotates it causes the balls to rotate as well. Because the balls are rolling they have a much lower coefficient of friction than if two flat surfaces were sliding against each other. Ball bearings tend to have lower load capacity for their size than other kinds of rolling-element bearings due to the smaller contact area between the balls and races. However, they can tolerate some misalignment of the inner and outer races. History Although bearings had been developed since ancient times, the first m ...
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Oloid
An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the edge of the other circle. The distance between the circle centers equals the radius of the circles. One third of each circle's perimeter lies inside the convex hull, so the same shape may be also formed as the convex hull of the two remaining circular arcs each spanning an angle of 4π/3. Surface area and volume The surface area of an oloid is given by:. :A = 4\pi r^2 exactly the same as the surface area of a sphere with the same radius. In closed form, the enclosed volume is :V = \frac \left(2 E\left(\frac\right) + K\left(\frac\right)\right)r^, where K and E denote the complete elliptic integrals of the first and second kind respectively. A numerical calculation gives :V \approx 3.0524184684r^. Kinetics The surface of the ...
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Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into ''static friction'' (" stiction") between non-moving surfaces, and ''kinetic friction'' between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1). *Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. *Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. *Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. *Internal friction is the force resisting motion between the elements making up a ...
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Developable Roller
In geometry, a developable roller is a convex solid whose surface consists of a single continuous, developable face. While rolling on a plane, most developable rollers develop their entire surface so that all the points on the surface touch the rolling plane. All developable rollers have ruled surfaces. Four families of developable rollers have been described to date: the prime polysphericons, the convex hulls of the two disc rollers (TDR convex hulls), the polycons and the Platonicons. Construction Each developable roller family is based on a different construction principle. The prime polysphericons are a subfamily of the polysphericon family. They are based on bodies made by rotating regular polygons around one of their longest diagonals. These bodies are cut in two at their symmetry plane and the two halves are reunited after being rotated at an offset angle relative to each other. All prime polysphericons have two edges made of one or more circular arcs and four verti ...
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Dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating or entertainment. History Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the pract ...
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Land Vehicle
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), watercraft (ships, boats, underwater vehicles), amphibious vehicles (screw-propelled vehicles, hovercraft), aircraft (airplanes, helicopters, aerostats) and spacecraft.Halsey, William D. (Editorial Director): ''MacMillan Contemporary Dictionary'', page 1106. MacMillan Publishing, 1979. Land vehicles are classified broadly by what is used to apply steering and drive forces against the ground: wheeled, tracked, railed or skied. ISO 3833-1977 is the standard, also internationally used in legislation, for road vehicles types, terms and definitions. History * The oldest boats found by archaeological excavation are logboats, with the oldest logboat found, the Pesse canoe found in a bog in the Netherlands, being carbon dated to 804 ...
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Reuleaux Triangle
A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular disks, each having its center on the boundary of the other two. Constant width means that the separation of every two parallel supporting lines is the same, independent of their orientation. Because its width is constant, the Reuleaux triangle is one answer to the question "Other than a circle, what shape can a manhole cover be made so that it cannot fall down through the hole?" Reuleaux triangles have also been called spherical triangles, but that term more properly refers to triangles on the curved surface of a sphere. They are named after Franz Reuleaux,. a 19th-century German engineer who pioneered the study of machines for translating one type of motion into another, and who used Reuleaux triangles in his designs. However, these shapes were known before his time, for instance by the ...
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